4 problems

Song's conjecture. For an arbitrary hyperkähler variety, the norm of the line class satisfies

Let $X$ be an irreducible holomorphic symplectic manifold, let $Y$ be a smooth hypersurface in $X$, and let $F$ be the characteristic foliation on $Y$. Let $q$ be the Beauville–Bog…

Characteristic-foliation conjecture. If $q(Y,Y)>0$, a general leaf of $F$ is Zariski dense in $Y$; if $q(Y,Y)=0$, the Zariski closure of a general leaf of $F$ is an abelian variety…

Tyurin–Bogomolov–Hassett–Tschinkel–Huybrechts–Sawon conjecture.